484 NOTES.

other's bold, resolved, settled upon general conclusions, and in them, if we will believe his friend, dogmatical." The distinctive characteristics of the two thinkers are here, as Dr. Tonnies remarks, excellently given in terms that might have come from Hobbes himself. I am less sure that Dr. Tonnies is right when he goes on, in the same note, to express his conviction that the words of Hobbes^ in the " Ep. ded." to the De Corpore when, after lauding Copernicus, Galileo and Harvey, he says : " Ante hos nihil certi in physica erat praeter experimenta unicuique sua et historias naturales, si tamen et hae dicendae certae sint, quae civilibus historiis certiores non sunt " directly point to Bacon's Sylva Sylvamm, or a Natural History in Ten Centuries [of Experiments], published according to him, in first Latin edition, in 1648, not long before the De Corpore. Leaving aside a ques- tion as to this date, and going back to the first publication in 1627, we are still left with the difficulty of understanding how Bacon's Natural History can be described as prior ("ante hos ") to the work done by Galileo, to say nothing of Copernicus. It seems more natural to suppose that the reference is back to the ancients. EDITOR. THE METHOD OF MEASURING PROBABILITY AND UTILITY. " Previous to the time of Pascal, who would have thought of measuring doubt and belief?" writes Jevons, contending that the measurement of utility may one clay cease to be paradoxical. The analogy indicated by Jevons I have attempted to trace in a recently-published little study (mentioned above, p. 466) on the Art of Measurement, which it is the object of the following lines to describe. One feature of resemblance between the compared sciences is that in both some of the data are apt to be very rough, more removed from the possibility of numerical precision than is usual in the Mathematical Sciences. In Probabilities, when we seek to ascend from an observed event to its cause, in the way described by Mill after Laplace (Logic, bk. iii., ch. 18, 5, 6), there frequently occurs a constant representing " a priori probability," concerning which, as Mill says, we "cannot form any plausible conjecture, much less appreciate it numerically". The regular constructions of mathematical reasoning repose upon the loose foundations of common-sense. There is a similar mixture of materials in Economical Science. Abstract reasoning must cohere with practical wisdom. In Probabilities it is often necessary to assume that quantities between which no inequality has obtruded itself in the course of experience may be treated as equal. Thus, in the Theory of Observations the most tri- umphant application of the Calculus it is virtually postulated that one value of the object under measurement is a priori as probable as another. In Utilitarian Theories, Equality is similarly postulated. The reasoning of Bentham and Prof. Sidgwick, that equality of distribution tends to maxi- mum happiness, presupposes that the distributees are equally capable of happiness. The Mathematical Theory of Observations is comparable with the principle of Authority in Social Science. The physicist, when there are given to him different estimates of a quantity, does not usually reject any, nor yet does he entirely accept any. He forms a Weighted Mean between the data, a combination of the evidence in which more importance is assigned to those sources of information which, in past experience, have proved more accurate. The social philosopher should proceed similarly with regard to that large portion of his subject-matter which is not amen- able to Inductive Method where we have only indistinct and fallible